Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 954-983 |
| Seitenumfang | 30 |
| Fachzeitschrift | SIAM Journal on Mathematical Analysis |
| Jahrgang | 49 |
| Ausgabenummer | 2 |
| Publikationsstatus | Veröffentlicht - 2017 |
| Extern publiziert | Ja |
Abstract
We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for ut = uΔu + u ∫Ω |∇u|2 in bounded domains Ω ⊂ ℝn which arises in game theory. We prove that solutions converge to 0 if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with Ω; i.e., the finite-time blow-up is global.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: SIAM Journal on Mathematical Analysis, Jahrgang 49, Nr. 2, 2017, S. 954-983.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On a degenerate nonlocal parabolic problem describing infinite dimensional replicator dynamics
AU - Kavallaris, Nikos I.
AU - Lankeit, Johannes
AU - Winkler, Michael
PY - 2017
Y1 - 2017
N2 - We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for ut = uΔu + u ∫Ω |∇u|2 in bounded domains Ω ⊂ ℝn which arises in game theory. We prove that solutions converge to 0 if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with Ω; i.e., the finite-time blow-up is global.
AB - We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for ut = uΔu + u ∫Ω |∇u|2 in bounded domains Ω ⊂ ℝn which arises in game theory. We prove that solutions converge to 0 if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with Ω; i.e., the finite-time blow-up is global.
KW - Blow-up
KW - Degenerate diffusion
KW - Evolutionary games
KW - Infinite dimensional replicator dynamics
KW - Nonlocal nonlinearity
UR - http://www.scopus.com/inward/record.url?scp=85018724882&partnerID=8YFLogxK
U2 - 10.1137/15M1053840
DO - 10.1137/15M1053840
M3 - Article
AN - SCOPUS:85018724882
VL - 49
SP - 954
EP - 983
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 2
ER -